If purely inferential introduction and elimination rules fix a semantic value for ∃, then analogous rules fix the same semantic value for W

The notion of determination of semantic value in a well-defined semantic framework is, at least, clear—unlike the general notion of determination of sense. However, as Gómez-Torrente points out, by concentrating on the fixation of reference (or semantic value) rather than sense, Hacking opens himself up to an objection not unlike the objection to permutation-invariance approaches we considered above (see also Sainsbury 2001, 369). Consider the quantifier \(\dq{W}\), which means “not for all not